⚛️ high-energy theory

Quantum Vacuum energy as the origin of Gravity

This paper proposes that gravity originates from quantum vacuum energy, leading to an environmental and scale-dependent Newton's constant that resolves the Big Bang singularity, reinterprets black hole entropy, and potentially explains the Hubble tension within a symmetric cosmological model.

Original authors: André LeClair

Published 2026-07-14

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: André LeClair

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe not as a stage where gravity acts like a puppet master, but as a giant, invisible ocean. In this ocean, there's a constant, bubbling energy even when nothing else is there. This is the Quantum Vacuum. For over a century, physicists have treated gravity as a fundamental force, like a rule written in the stars that never changes. But this paper asks a wild question: What if gravity isn't a rule at all, but a ripple caused by that bubbling ocean?

The author, André LeClair, suggests that gravity is actually an "induced" effect, much like how a trampoline bends under a heavy ball. But instead of a ball, the "weight" comes from the vacuum energy itself.

The Gravity That Isn't "Constant"

Here's the twist: In our everyday world, we think Newton's constant ( $G_N$ )—the number that tells us how strong gravity is—is a fixed, unchangeable fact of nature, like the speed of light. This paper argues that $G_N$ is actually "environmental."

Think of it like the temperature in a room. If you open a window, the temperature changes. Similarly, the author suggests that the strength of gravity depends on the "temperature" of the universe, which is tied to how big the universe is and how much stuff is in it.

The Formula: The paper proposes a specific relationship: $G_N = c^2 R_\infty / 2M_\infty$ .
The Analogy: Imagine gravity isn't a rigid law, but a rubber band. The more the universe stretches (grows in size $R_\infty$ ) and the more energy it holds ( $M_\infty$ ), the tighter or looser that rubber band gets.

The "Big Swing" Instead of the "Big Bang"

This is where things get really fun. The standard story of the universe says it started with a Big Bang, a moment of infinite density and a "singularity" where physics breaks down (like a math error on a calculator).

This paper suggests that the Big Bang never happened. Instead, the universe is more like a giant pendulum or a swing.

The Past: Long ago, the universe was huge and expanding, but then it started to slow down and swing back in, compressing.
The Bottom of the Swing: It didn't crush down to a tiny, infinite point (a singularity). It stopped at a tiny, but finite, size called $a_{min}$ .
The Future: After hitting this bottom, it swung back out, expanding again into the universe we see today.

The paper calculates that the universe never gets smaller than a specific tiny size: $a_{min} \approx e^{-1/bb}$ . Based on current data, this is roughly $2 \times 10^{-22}$ .

The Result: Because the universe never hits zero size, there is no "geometric curvature singularity." The math stays clean, and the universe is eternal, swinging back and forth forever.

Solving the "Hubble Tension" Mystery

Right now, astronomers are confused. They measure how fast the universe is expanding (the Hubble constant, $H_0$ ) in two ways:

Looking at nearby stars (Supernovae): They get a value of about 73.0 km/s/Mpc.
Looking at the ancient light from the Big Bang (CMB): They get a value of about 67.4 km/s/Mpc.

These numbers don't match, and it's a huge headache for physicists. This paper suggests the answer is simple: Gravity changes over time.

When we look at the ancient light (high redshift, $z \approx 1100$ ), gravity was slightly weaker because the universe was "hotter" and smaller.
When we look at nearby stars (low redshift, $z \approx 0$ ), gravity is slightly stronger.
The paper suggests a parameter $bb \approx 0.02$ explains this difference. If you plug this number in, the two measurements actually agree!

The "Bits" of the Universe

The paper also rethinks what "information" means in a black hole or the edge of the universe. Usually, we think of space itself being made of tiny pixels. This paper suggests a different idea: The "bits" of information are just massless particles (like photons) sitting at the edge of the universe.

If the universe has a radius $R_\infty$ , these particles have a wavelength of $\lambda = 2\pi R_\infty$ .
It's like the edge of the universe is a giant drum, and the "bits" are the vibrations on that drum. This gives a new, simpler way to calculate the entropy (disorder) of the universe without needing to assume space itself is pixelated.

What About the "Before"?

If the universe is a swing, what was it doing before it swung down?

The paper suggests that inflation (a theory that the universe expanded super-fast right after the Big Bang) might not be necessary.
Why? Because the universe was already hot, flat, and expanded when it hit the bottom of the swing ( $a_{min}$ ). The "swing" itself does the job that inflation was supposed to do.
The paper notes that the maximum redshift (how far back we can see) in this model is around $z_{max} \approx 5 \times 10^{21}$ , which is a temperature of about $10^{22}$ K. This is hot enough to explain the early universe without needing a "Big Bang" singularity.

Is This Proven?

The authors are careful. They don't claim to have "solved" gravity.

It's a proposal: They suggest that if you assume gravity comes from vacuum energy, and if you assume a specific formula for that energy (involving a particle mass $m_z$ and a coupling $g$ ), then everything fits together nicely.
The Evidence: The idea is "well-motivated" by previous work on quantum field theory, but it's still a hypothesis.
The Test: The paper points out that if this is true, gravity should get slightly weaker as things get hotter. They mention some old, small-scale experiments where weights were measured at different temperatures. Those experiments showed a tiny decrease in weight as temperature went up, which matches the paper's prediction (though the data is rough).
The Future: The authors suggest that if we can measure how gravity changes with temperature in a lab (a "bench-top" experiment), we could prove or disprove this idea.

The Bottom Line

This paper offers a playful but serious alternative to the standard story. It says: Gravity isn't a fundamental force; it's a side effect of the quantum vacuum. The universe didn't start with a bang; it started with a swing. And the reason we can't agree on how fast the universe is expanding is that gravity itself is changing as the universe swings back and forth.

It's a fresh way to look at the cosmos, turning the "Big Bang" into a "Big Swing" and suggesting that the rules of the game are written by the players themselves.

Technical Summary: Quantum Vacuum Energy as the Origin of Gravity

Problem Statement
The paper addresses the fundamental lack of understanding regarding the origin of gravity and the persistence of classical singularities (e.g., the Big Bang and black hole centers) within General Relativity (GR). While Quantum Mechanics (QM) and GR are established, a complete theory of quantum gravity remains elusive. The authors propose a radical alternative: rather than quantizing the gravitational field (gravitons), gravity itself may emerge from the quantum vacuum energy density ( $\rho_{vac}$ ) of matter and radiation fields in flat Minkowski space. The central hypothesis is that Newton's constant ( $G_N$ ) is not a fundamental constant but an environmental parameter derived from the total mass-energy and size of the universe, potentially resolving the Hubble tension and avoiding the $a(t)=0$ singularity.

Methodology
The authors employ a semi-classical framework where the gravitational field is not quantized, but the vacuum energy is treated using modern Quantum Field Theory (QFT) and Renormalization Group (RG) techniques. The methodology proceeds through several distinct steps:

Gravitational Casimir Effect: The authors formulate a heuristic gravitational analog to the electromagnetic Casimir effect. By treating the cosmic horizon as "conducting plates" in a vacuum, they derive the emergence of Einstein's field equations (specifically Friedmann's equations) without assuming GR a priori. This leads to a specific identification of Newton's constant: $G_N = c^2 R_\infty / 2M_\infty$ , where $R_\infty$ and $M_\infty$ are the horizon radius and total vacuum mass-energy of the universe.
Vacuum Energy Formula: The study adopts a specific, well-motivated formula for $\rho_{vac}$ derived from integrable QFTs and the thermodynamic Bethe ansatz: $\rho_{vac} \propto m_z^4 / g$ . Here, $m_z$ is the mass of the lightest particle, and $g$ is a dimensionless coupling constant.
Induced RG Flow: The authors assume $g$ is a marginally irrelevant coupling with a 1-loop beta function ( $\mu \partial_\mu g \propto g^2$ ). Since $\rho_{vac}$ depends on $g$ , this induces an effective RG flow for $G_N$ as a function of the energy scale $\mu$ .
Cosmological Mapping: The energy scale $\mu$ is tied to the cosmological temperature $T(t)$ and redshift $z$ via $\mu \propto T \propto (1+z)$ . This renders $G_N$ time-dependent: $G(t) = G_N (1 + b_b \ln a(t))$ , where $b_b$ is a small RG parameter.
Exact Solutions: The modified Friedmann equations are solved exactly for a "dark-universe" (vacuum energy only) and subsequently for the $\Lambda$ CDM model (including matter and radiation).

Key Contributions and Results

Emergence of Gravity: The paper demonstrates that Friedmann's equations can be derived from a gravitational Casimir effect driven by $\rho_{vac}$ , suggesting gravity is an emergent phenomenon of the quantum vacuum rather than a fundamental force requiring quantization.
Reinterpretation of Entropy: The formula for $G_N$ allows for a reinterpretation of the Gibbons-Hawking (de Sitter) and Bekenstein-Hawking (black hole) entropies. Instead of quantized spacetime pixels, the entropy "bits" are interpreted as quantized massless particles (e.g., photons) at the horizon with wavelength $\lambda = 2\pi R_\infty$ .
Resolution of the Big Bang Singularity: The induced RG flow leads to a minimal scale factor $a_{min} = e^{-1/b_b}$ . The solution for the scale factor $a(t)$ is an "inverted Gaussian" (or "Gaussian de Sitter") that never reaches zero. The universe undergoes a smooth transition from a contracting phase to an expanding phase at $t_{min}$ , avoiding the geometric curvature singularity at $a=0$ . The "Big Bang" is reinterpreted as a "Hot Big Bang" occurring at the point of minimum scale factor, with the universe's age being effectively infinite.
Explanation of the Hubble Tension: The time-dependence of $G_N$ offers a resolution to the discrepancy between local ( $z \approx 0$ ) and early-universe ( $z \approx 1100$ ) measurements of the Hubble constant ( $H_0$ ). Because $G_N$ decreases at higher energy scales (higher $z$ ), measurements from the Cosmic Microwave Background (CMB) infer a lower $H_0$ compared to local supernovae. The model constrains the RG parameter to $b_b \approx 0.02$ , which aligns with the observed tension.
Symmetry and Oscillation: The solution exhibits a symmetry $a(t) = a(-t + 2t_{min})$ , suggesting the universe oscillates like a pendulum between infinite expansion and contraction, with the current epoch being on the "upswing."

Significance and Claims
The authors claim that this framework provides a novel, semi-classical approach to cosmology that addresses profound open problems without invoking a full theory of quantum gravity. Specifically:

It explains the value of $G_N$ as an environmental quantity dependent on the universe's total mass and size.
It resolves the Big Bang singularity naturally through the RG flow of $G_N$ , obviating the need for inflationary mechanisms to smooth out a singularity (though it acknowledges the need to explain primordial fluctuations).
It provides a potential physical mechanism for the Hubble tension, linking the discrepancy to the energy-scale dependence of Newton's constant.
It predicts that $G_N$ depends on temperature, a claim supported by the authors' analysis of existing, albeit limited, bench-top experiments measuring weight changes with temperature.

The paper remains modest regarding the identification of the specific particle with mass $m_z$ (suggesting Majorana neutrinos as a candidate) and acknowledges that the UV completeness of the underlying QFT (due to the Landau pole) is a separate issue from the UV incompleteness of quantum gravity, which the model successfully bypasses in the cosmological evolution. The authors emphasize that their results are consistent with current observational data, including supernovae trends and bounds on the time-variation of $G_N$ , while offering testable predictions for future experiments.